Word of caution: If it's truly an antique and is in working order, upcycling the fridge may not be in your best interests. Depending on how you upcycle it, you may have to make irreversible changes to the fridge which could lower it's potential value. Definitely double-check with someone specialising in antique appliances first.
With that out of the way, here's a few options you might consider:
Bar fridge - More of a 'reuse' rather than upcycling, but a lot of people like to use older fridges in their home bar/rumpus/cave/den or other entertaining space, as a place to chill drinks and party food when they have guests over, turning it off when they aren't using it to save on power.
If the fridge still works (or only needs cleaning/minor repairs/re-gassing), it would be more economical to keep it in service, whether at yours or a family member's / close friend's place. If it has been sitting for a while, do have an appliance repair person inspect the fridge before powering it on first!
Cabinet or Pantry - This one is probably the most obvious choice and doesn't require much in the way of alteration - use it in the kitchen, laundry, or den as a place to store dry stuff.
Bookshelf or Storage Nook - Another one that doesn't require much alteration. If you want the shelves to be visible, you could take the door off, or place the fridge in a corner and prop it open along the wall, so it still looks like a fridge but the door doesn't get in the way.
Planters and Garden Bed - The door shelves could be used as small planters, and the main fridge section could be used as a raised garden bed. Or, you could keep it upright and use the shelves as a space to grow your seedlings and tender crops.
Poolside/Outside storage - need a place for your pool towels, plastic cups and plates, kids toys, and party supplies? It means less worry about forgetting your towels inside, and more free space in the inside closets.
Wine cellar/Whisky cabinet - with some nice custom wooden shelving, you could use the fridge as a cool, dry place to store your best bottles of booze. Painting the insides a darker colour, or continuing the wood up the sides and back can add to the effect.
Doghouse - I once saw a fridge on it's side, with the door held open with poles like a veranda roof and a dog bed inside. Probably better for small to medium sized-dogs.
If you do go down the route of upcycling it in a way that doesn't require powering it on, I would recommend getting it de-gassed. As LShaver mentioned in the comments - it's likely that the old refrigerant is harmful to the environment, so that should be removed and disposed of correctly.
You could potentially even re-sell the mechanical parts (like the compressor and coils) as spares, or as a last resort, take them to a scrap metal recycling facility to save them from landfill.